1-Main contribution:

This manuscript presents a 2-D FE modelling study on the impact of stress magnitude and orientation on the bulk permeability of shallow-water carbonate rock displaying different sets of fractures. The novelty consists of considering a succession of major tectonics events over a geological period (Middle Triassic subsidence followed by Neogene Alpine compression) while simulating fracture behaviour, more specifically aperture change. A total of five horizontal transects illustrating the complexity of the fractured systems are collected in the Latemar platform, an outcrop analogue for hydrocarbon reservoirs as well as thermal energy and CO₂ storage. The scale of investigation is sub-seismic, thereby providing crucial information for engineers on the physical processes influencing the flow behaviour of reservoir and storage sites. Each section of the manuscript is well-written and well-structured. The results and interpretations introduced in the text are supported by the figures and data, while the assumptions considered during the simulations are clearly stated. There are few major and minor items that should be addressed as shown below.

2-Major items:

• Introduction (Lines 156-159): Previous simulation works taking into account superimposed tectonics events have “not been well-represented”. What do the authors mean here? Do they mean that no study was carried out on the topic or that the quality of the previous studies is too poor? Please be more specific by introducing few references and by explaining why those studies were not properly carried out.
• Line: 328: Simulations are run in the 2-D domain. Please specify this in the abstract.
• Line 341, Equation 3: Please specify the friction coefficient(s) assigned to the fractures and ideally, justify these values based on published works.
• Line 411: The matrix permeability is assumed constant and equal to 2 mD based on Whitaker et al. (2014)’s work. However, this later work shows that a large number of deposits have a permeability ranging between 50 mD and 5000mD (Fig. 7 in Whitaker et al). Could the authors explain selecting such low value? Besides, the mean effective permeability of each FSS ranges between 0.85 and 3.24 mD (see Table 2 and Lines 608-613 in the submitted manuscript). Does it mean that fractures in the platform top have minor to negligible impact on overall bulk rock permeability if considering higher permeability for the host rock? Is there any published permeability measurement from the Latemar platform? If so, please add it in the methodology section for comparison purposes.
• In the methodology section 3.1 (Line 295): The magnitude of the two far-field stress regimes is assumed. Which criteria these assumptions are based on? In line 475, it is mentioned that those boundary conditions are “feasible” for modelling compressive settings. Please be more specific on what “feasible” means here.
• Stylolites are assumed as flow conduits despite controversy on the topic as stated in Line 297. The simulation results and conclusions on the enhanced bulk permeability caused by stress-induced fracture opening (Line 877) are thus optimistic and this should be stressed in the conclusion. Note that the assumed low permeability of the host rock (2 mD) as discussed in the previous comments also adds to the overall key impact of fracture on increased permeability reported in the submitted manuscript.

3- Minor items:

• Lines 122-124: Odd grammatical structure of the sentence. Please rephrase.
• Lines 125-126: If possible, please add any practical examples of change in the flow pattern of reservoirs or storage sites caused by stress changes during injection/extraction of fluids. This would strengthen the relevancy of this work.
• Section 3.1.1: The methodology to collect data on fractures are well described. What about the stylolites? Were they also collected using the same methods? Could you add information about this in this section?
• Line 413: Add full stop at the end of the sentence.
• Fig 8: Do the minimum and maximum horizontal stress equal? I have not seen information about it so far. If both stresses are different, it would be good to add a plot displaying the evolution of S_h and S_H with time throughout the simulation period.
• There are three publications of Bisdom et al., 2016. The reference “Bisdom et al., 2016c” is missing in the manuscript (see Lines 672, 741, 747, and 799).

I recommend minor revision.

Best regards,

Frédéric Amour

DTU Offshore

Denmar

General Comments

The paper to investigate the impact of stress regime change on permeability in complex fractured systems starting form outcrops as an analogue of the subsurface reservoirs. The paper is very interesting and well-structured with a very interesting modelling exercise.

I have no concerns about the strength of the model itself, I only found sometimes difficult to clearly see the constrains on the input parameters and thus some of the conclusions could be arguable to me.

In particular, authors infer the tectonic stress from fracture orientation, however no crosscutting relations nor a proper description of the fractures are presented making the assumptions on stress orientation not well constrained to me.

More in general, the input parameters (mechanical data, fracture aperture, matrix permeability, stress magnitudes etc.), of the modelling exercise should be clarified. The feeling I have is that the authors put a lot of efforts in building a very nice modelling, however the starting data seem to be more assumed that actually verified and constrained.

The presented investigation uses the outcropping network geometry as input for geomechanical and flow models, that is fair, but a key question could regard the timing of fractures formation. In my opinion the authors must clarify and show the evidence that relate the fracture formation to time. In other words, 1. what is the evidence that exclude very late (i.e. during exhumation) formation of some of the observed fractures? And 2. Since no crosscutting relationship are analyzed, why should we think that all fractures experienced both tectonic stress regimes?

Specific comments

Line 255 “the arrangements orientations and the stress fields during the development of the fractures are documented”. Stress inversion technique must be explained here.

Line 257 “In the Valsorda Valley (Fig. 3), carbonate outcrops are affected by minor reverse conjugate faults dipping at low angle (< 30o) to bedding.” I strongly suggest the authors to clearly show displacements and kinematic indicators supporting this.

Line 262 “On the other side, at the flat-topped Latemar, on the sub-horizontal (pavement) outcrops, fractures also form conjugate patterns, exhibiting dextral and sinistral displacements (Figs. 3 and 5).” I think that authors should highlight this evidence in figure 3 and 5.

Line 286 “Overall, two deformation phases were observed and documented” I think that authors must better document this.

Line 298 “Although stylolite tends to hinder fluid flow (Boersma et al., 2019), observations in figures 3, 4 and 5 show they can enhance fluid movement”. Even if I do think that stylolite generally hinder fluid flow I would suggest reading the paper by Heap et al., 2018 were it is proposed that stylolites can be considered as conduits for flow. I would also ask the authors to clearly describe and show the observations in figures 3, 4 and 5 proving that they can enhance fluid movement.

Line 321 “Slight modifications and/or extrapolations of the fracture's original pattern were implemented to maintain the fracture topological connectivity” I would ask the authors to be more specific .

Line 338 “When the fracture is in a closure condition, and sufficient loading is acting in the tangential direction, the fracture may slip. The slip and stick conditions of the fracture are determined based on the classical Coulomb's friction law”. Coulomb friction depends on several parameters and it can greatly vary form host rock to host rock (see Collettini et al., 2019). It would be appropriate to have more information about the adopted mechanical properties.

Line 411 “We have adopted the matrix permeability value of 2 x 10-15 m “ Are there any other constrain eventually based of data from actual samples of the Latemar area or from similar lithologies?

Line 437 “These tectonic episodes are constrained to the NW-SE and N-S shortening (compressive) directions with an assumed maximum magnitude of 50 and 160 MPa for the subsidence-related and Alpine deformation stages, respectively.” I can’t really see how authors constrain these stress values. Authors successively state that they refer to the The World  Stress Map database, however as far as I know that paper is more focused on stress orientation that stress magnitude, moreover here there is no mention about the assumed depth so I found these stress values not clear. An explanation is given only at line 625, I think that it would be better to report and exlpain here the used input values.

Line 445 “The constitutive parameter values are Youngs modulus 25 GPa and Poisson ration 0.30 (see Table 1 for detailed parameters).” Once again I would like the authors to specify where these input data come from. Moreover, if perfect elasticity is supposed in the model and dynamic parameters are used, they can differ a lot from static ones in particular for dolostone samples (see Trippetta et al., 2013). In any case a reference for such used values must be given.

Suggested Complete References

Collettini, C., Tesei, T., Scuderi, M.M., Carpenter, B.M., Viti, C., 2019. Beyond Byerlee friction, weak faults and implications for slip behavior. Earth Planet. Sci. Lett. 519, 245–263. https://doi.org/10.1016/j.epsl.2019.05.011

Heap, M., Reuschlé, T., Baud, P., Renard, F., Iezzi, G., 2018. The permeability of stylolite-bearing limestone. J. Struct. Geol. 116, 81–93. https://doi.org/10.1016/j.jsg.2018.08.007

Trippetta, F., Collettini, C., Meredith, P.G., Vinciguerra, S., 2013. Evolution of the elastic moduli of seismogenic Triassic Evaporites subjected to cyclic stressing. Tectonophysics 592, 67–79.

Technical corections

Scales are absent in figures 1d and e

I have a problem also with the scales in figures 3 A and B. According to the shown scales outcrops are ~ 500 m long each. It is correct? Moreover the legend must be improved, I can’t really distinguish between Tectonic styliolites and Perp. fractures

Line 255 and sub-horizontal (pavement) outcrops. Maybe “that” is missing here